Reactions controlled by enhanced diffusion: Deterministic and stochastic approaches

G. Zumofen; J. Klafter; M. F. Shlesinger

doi:10.1016/S0301-0104(96)00219-4

Reactions controlled by enhanced diffusion: Deterministic and stochastic approaches

G. Zumofen^*, J. Klafter, M. F. Shlesinger

^*Corresponding author for this work

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Abstract

We study the transient A + B → 0 reaction at stoichiometric conditions in dimensions d = 1, 2, and 3. The particles are assumed to follow enhanced diffusion resulting from Lévy walks characterized by the index 1 < γ ≤ 2. Particle density decays and particle-particle correlation functions are calculated using deterministic reaction diffusion equations and a stochastic model based on random walks. In particular we concentrate on the breakdown of the Ovchinnikov-Zeldovich segregation phenomenon. Segregation is shown to disappear in d = 3 dimensions under enhanced diffusion conditions for γ < 3/2. The erosion of the segregation is an example of Lévy mixing.

Original language	English
Pages (from-to)	89-98
Number of pages	10
Journal	Chemical Physics
Volume	212
Issue number	1 SPEC. ISSUE
DOIs	https://doi.org/10.1016/S0301-0104(96)00219-4
State	Published - 15 Nov 1996

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title = "Reactions controlled by enhanced diffusion: Deterministic and stochastic approaches",

abstract = "We study the transient A + B → 0 reaction at stoichiometric conditions in dimensions d = 1, 2, and 3. The particles are assumed to follow enhanced diffusion resulting from L{\'e}vy walks characterized by the index 1 < γ ≤ 2. Particle density decays and particle-particle correlation functions are calculated using deterministic reaction diffusion equations and a stochastic model based on random walks. In particular we concentrate on the breakdown of the Ovchinnikov-Zeldovich segregation phenomenon. Segregation is shown to disappear in d = 3 dimensions under enhanced diffusion conditions for γ < 3/2. The erosion of the segregation is an example of L{\'e}vy mixing.",

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T2 - Deterministic and stochastic approaches

AU - Zumofen, G.

AU - Klafter, J.

AU - Shlesinger, M. F.

PY - 1996/11/15

Y1 - 1996/11/15

N2 - We study the transient A + B → 0 reaction at stoichiometric conditions in dimensions d = 1, 2, and 3. The particles are assumed to follow enhanced diffusion resulting from Lévy walks characterized by the index 1 < γ ≤ 2. Particle density decays and particle-particle correlation functions are calculated using deterministic reaction diffusion equations and a stochastic model based on random walks. In particular we concentrate on the breakdown of the Ovchinnikov-Zeldovich segregation phenomenon. Segregation is shown to disappear in d = 3 dimensions under enhanced diffusion conditions for γ < 3/2. The erosion of the segregation is an example of Lévy mixing.

AB - We study the transient A + B → 0 reaction at stoichiometric conditions in dimensions d = 1, 2, and 3. The particles are assumed to follow enhanced diffusion resulting from Lévy walks characterized by the index 1 < γ ≤ 2. Particle density decays and particle-particle correlation functions are calculated using deterministic reaction diffusion equations and a stochastic model based on random walks. In particular we concentrate on the breakdown of the Ovchinnikov-Zeldovich segregation phenomenon. Segregation is shown to disappear in d = 3 dimensions under enhanced diffusion conditions for γ < 3/2. The erosion of the segregation is an example of Lévy mixing.

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JO - Chemical Physics

JF - Chemical Physics

IS - 1 SPEC. ISSUE

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Reactions controlled by enhanced diffusion: Deterministic and stochastic approaches

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